Basics calculator

RC time constant

Τ = 1 ms, fc = 159 Hz with 10 kΩ and 100 nF

A capacitor fills like a bucket through a straw: fast at first, then slower.

Opens in the app on 1 December, with Circuit Notebook 1.0 See it worked out

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The example, worked out

Given

Resistance R: 10 kΩ
Capacitance C: 100 nF
Step voltage: 5 V
Level of interest: 50 %

Working

ohms times farads are seconds
where a filter made of them is 3 dB down
to reach 50 % of the step

Results

Time constant τ1 ms

Cutoff (−3 dB)159 Hz

To 50 % (2.5 V)693 µs

To 63 % (τ)1 ms

To 95 % (3 τ)3 ms

To 99 % (5 τ)5 ms

The formulas

τ = R × Cohms times farads are seconds
fc = 1 / (2π R C)where the RC filter is 3 dB down
t = −τ ln(1 − x)the time to reach the share x of the step

The usual traps

63 % at one τ, not 100 %: five τ for 99 %.
Charging and discharging take the same time.

Questions

How do I calculate the time constant of an RC circuit?

τ = R × C: ohms times farads are seconds. fc = 1 / (2π R C): where the RC filter is 3 dB down. t = −τ ln(1 − x): the time to reach the share x of the step.

What does it give for typical values?

Τ = 1 ms, fc = 159 Hz with 10 kΩ and 100 nF. Time constant τ: 1 ms; Cutoff (−3 dB): 159 Hz.

What are the usual mistakes?

63 % at one τ, not 100 %: five τ for 99 %. Charging and discharging take the same time.

In the app

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The part you can buy

Results rounded to standard values (E12, E24, E96) and power ratings.

The working, shown

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Into your notebook

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Opens in the app on 1 December, with Circuit Notebook 1.0

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